How can I turn this math formula into a 3d model?
I guess you could, but I can't think of efficient way of doing it. Your snowman is a procedural geometry, when most of the 3d computer graphics are based on triangles.
I think problem will be the precision, especially those equations describe volume rather than surface.
I've made quick test for the lemon from surfer example:

import bpy
import math

for x_ in range (-20,20):
    for y_ in range (-20,20):
        for z_ in range (-20,20):
            x = x_*0.05
            y = y_*0.05
            z = z_*0.05
            left = x**2 + z**2
            right = y**3*(1-y)**3

            if left-right&lt;=0.05:
                bpy.ops.mesh.primitive_uv_sphere_add(segments=3, ring_count=3, radius=0.005, enter_editmode=False, align='WORLD', location=(x, y, z))


you could probably generate a point cloud, and then use Meshlab or CloudCompare to reconstruct the mesh from point cloud